Relative uncertainties in the preparation of analytical solutions

Analytical error

As guidance to minimise errors in the preparation of analytical solutions, Table 1, giving estimations of the relative uncertainty, is to be consulted.

In order to avoid either the use of extremely low amounts or an unnecessarily large expenditure of solvents, a dilution series will often have to be prescribed for the preparation of dilute solutions used particularly for spectrophotometry measurement. In this context not all combinations of (usually 2 or 3) dilution steps will contribute equally to the random error of the dilution procedure.

If critical for the purpose, the optimal dilution is prescribed in consideration of the relative errors (capacity tolerance divided by nominal volume) associated with the various sizes of volumetric pipettes and volumetric flasks commonly used for these operations (taking the usual formula: square root of the sum of the squares of individual relative errors, to estimate the relative dilution error).

Tables giving the optimal number and nature of dilution steps needed to achieve a given dilution ratio, based upon given specifications for the capacity tolerances of volumetric glassware, are available in the literature.

For guidance see Table 2 (it is to be noted that these factors do not include reading errors).

Table 1 – Relative uncertainties in the preparation of analytical solutions

An uncertainty of 0.2 mg for the weighing procedure has been assumed for the calculations of the percentage relative uncertainties.

Table 2 – Relative errors for dilution with analytical glassware (pipettes P/flasks F)

Adapted from R.B. Lam and T.L. Isenhour, Minimising relative error in preparation of standard solutions by judicious choice of volumetric glassware, Analytical Chemistry, 1980, 53, 1158-1161.